No. When you're not playing nothing happens until you next load your game (at which point flowers wilt/weeds grow/mail is sent/etc). Villagers won't be effected.
Unless there was a villager planning on moving before you stopped playing. They will still leave on the date they were planning on moving ~ even if they never told you they were.
A new plot will still appear if the day after the last day you played a plot could have appeared.
Effectively it just acts as thoughh 1 day has passed, except for villagers leaving which take into account if the date has passed.
Both a friend and I, have had villagers move out when we didn't play for at least a week. That's how I lost Punchy.
I'm quite confused but thank you anyways!